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Recently, evolutionary coding agents powered by Large Language Models (LLMs) have emerged as powerful tools to automate this discovery process. In this work, we deploy one of such agentic frameworks, AlphaEvolve, to navigate the design spaces of two distinct game-theoretic paradigms: counterfactual regret minimization (CFR) and policy-space response oracles (PSRO). This automated search yielded two algorithms: Volatility-Adaptive Discounted (VAD-) CFR and Smoothed Hybrid Optimistic Regret (SHOR-) PSRO, which are consistently competitive with state-of-the-art human-designed baselines across an 18-game evaluation suite spanning Poker, Goofspiel, Liar's Dice, Blotto, and Battleship variants. 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